Description

The Product block outputs the result of multiplying two inputs: two
scalars, a scalar and a nonscalar, or two nonscalars that have the same dimensions. The
default parameter values that specify this behavior are:

Multiplication:Element-wise(.*)

Number of inputs:2

This table shows the output of the Product block for example inputs using default block parameter values.

Inputs and Behavior

Example

Scalar X
Scalar

Output the product of the two
inputs.

Scalar X
Nonscalar

Output a nonscalar having the same
dimensions as the input nonscalar. Each element of the output
nonscalar is the product of the input scalar and the corresponding
element of the input nonscalar.

Nonscalar X
Nonscalar

Output a nonscalar having the same
dimensions as the inputs. Each element of the output is the product
of corresponding elements of the inputs.

The Divide and Product of Elements blocks are variants
of the Product block.

The Product block (or the Divide block or Product
of Elements block, if appropriately configured) can:

Numerically multiply and divide any number of scalar, vector, or matrix
inputs

Perform matrix multiplication and division on any number of matrix
inputs

The Product block performs scalar or matrix multiplication, depending
on the value of the Multiplication parameter. The block
accepts one or more inputs, depending on the Number of
inputs parameter. The Number of inputs
parameter also specifies the operation to perform on each input.

The Product block can input any combination of scalars, vectors, and
matrices for which the operation to perform has a mathematically defined result. The
block performs the specified operations on the inputs, then outputs the result.

The Product block has two modes: Element-wise
mode, which processes nonscalar inputs element by element, and
Matrix mode, which processes nonscalar inputs as
matrices.

Element-Wise Mode

When you set Multiplication to
Element-wise(.*), the Product block is in
Element-wise mode, in which it operates on the individual
numeric elements of any nonscalar inputs. The MATLAB® equivalent is the .* operator. In element-wise
mode, the Product block can perform a variety of multiplication,
division, and arithmetic inversion operations.

The value of the Number of inputs parameter
controls both how many inputs exist and whether each is multiplied or divided to
form the output. When the Product block is in element-wise mode and
has only one input, it is functionally equivalent to a Product of Elements block. When the
block has multiple inputs, any nonscalar inputs must have identical dimensions, and
the block outputs a nonscalar with those dimensions. To calculate the output, the
block first expands any scalar input to a nonscalar that has the same dimensions as
the nonscalar inputs.

This table shows the output of the Product block for example inputs, using the indicated values for the Number of inputs parameter.

Parameter Values

Examples

Number of inputs:2

Number of inputs:*/

Number of inputs:/**/

Number of
inputs:**

Number of inputs:*/*

Matrix Mode

When the value of the Multiplication parameter is
Matrix(*), the Product block is in
Matrix mode, in which it processes nonscalar inputs as
matrices. The MATLAB equivalent is the * operator. In Matrix mode, the
Product block can invert a single square matrix, or multiply and
divide any number of matrices that have dimensions for which the result is
mathematically defined.

The value of the Number of inputs parameter
controls both how many inputs exist and whether each input matrix is multiplied or
divided to form the output. The syntax of Number of
inputs is the same as in element-wise mode. The difference between
the modes is in the type of multiplication and division that occur.

Expected Differences Between Simulation and Code Generation

For element-wise operations on complex floating-point inputs, simulation and code
generation results might differ in near-overflow cases. Although complex
numbers is selected and non-finite numbers is
not selected on the Code Generation > Interface pane of the Configuration Parameters dialog box, the code generator
does not emit special case code for intermediate overflows. This method improves the
efficiency of embedded operations for the general case that does not include extreme
values. If the inputs could include extreme values, you must manage these cases
explicitly.

The generated code might not produce the exact same pattern of
NaN and inf values as simulation when
these values are mathematically meaningless. For example, if the simulation output
contains a NaN, output from the generated code also contains a
NaN, but not necessarily in the same place.

Parameters

Main

Number of inputs — Control number of inputs and type of operation2 (default) | scalar | * or / for each input
port

Control two properties of the block:

The number of input ports on the block

Whether each input is multiplied or divided into the
output

When you specify:

1 or
* or
/

The block has one input port. In element-wise mode, the block
processes the input as described for the Product of
Elements block. In matrix mode, if the parameter
value is 1 or *, the block
outputs the input value. If the value is /,
the input must be a square matrix (including a scalar as a
degenerate case) and the block outputs the matrix inverse. See
Element-Wise Mode and Matrix Mode for more
information.

Integer value > 1

The block has the number of inputs given by the integer value.
The inputs are multiplied together in element-wise mode or
matrix mode, as specified by the Multiplication parameter. See Element-Wise Mode and Matrix Mode for more
information.

Unquoted string of two or more
* and /
characters

The block has the number of inputs given by the length of the
character vector. Each input that corresponds to a
* character is multiplied into the
output. Each input that corresponds to a /
character is divided into the output. The operations occur in
element-wise mode or matrix mode, as specified by the Multiplication parameter. See Element-Wise Mode and Matrix Mode for more
information.

Optimization of the code that you generate from the model. This
optimization can remove algorithmic code and affect the results of some
simulation modes such as SIL or external mode. For more information, see
Optimize using the specified minimum and maximum values (Simulink Coder).

Note

Output minimum does not saturate or clip the actual
output signal. Use the Saturation block instead.

Optimization of the code that you generate from the model. This
optimization can remove algorithmic code and affect the results of some
simulation modes such as SIL or external mode. For more information, see
Optimize using the specified minimum and maximum values (Simulink Coder).

Note

Output maximum does not saturate or clip the actual
output signal. Use the Saturation block instead.

Choose the data type for the output. The type can be inherited,
specified directly, or expressed as a data type object such as
Simulink.NumericType. For more information, see
Control Signal Data Types.

When you select an inherited option, the block behaves as
follows:

Inherit: Inherit via internal rule
— Simulink chooses a data type to balance numerical accuracy,
performance, and generated code size, while taking into account
the properties of the embedded target hardware. If you change
the embedded target settings, the data type selected by the
internal rule might change. For example, if the block multiplies
an input of type int8 by a gain of
int16 and
ASIC/FPGA is specified as the
targeted hardware type, the output data type is
sfix24. If Unspecified
(assume 32-bit Generic), in other words, a
generic 32-bit microprocessor, is specified as the target
hardware, the output data type is int32. If
none of the word lengths provided by the target microprocessor
can accommodate the output range, Simulink software displays an error in the Diagnostic
Viewer.

Inherit: Keep MSB– Simulink chooses a data type that maintains the full range
of the operation, then reduces the precision of the output to a
size appropriate for the embedded target hardware.

Tip

For more efficient generated code, deselect the
Saturate on integer overflow
parameter.

This rule never produces overflows.

Inherit: Match scaling– Simulink chooses a data type whose scaling matches the
scaling of the input types. If the full range of the type does
not fit on the embedded target hardware, the range is reduced
yielding a type appropriate for the embedded target hardware.
This rule can produce overflows. This rule does not support
multiplication between complex signals

The Inherit: Keep MSB and
Inherit: Match scaling rules do
not support multiplication between complex signals or signals
with non-zero bias. The rules support only multiplication and
division ('**', '*/',
'/*') between two inputs, matrix
multiplication of two inputs, and collapsing product of two
elements of a vector.

It is not always possible for the software to optimize code
efficiency and numerical accuracy at the same time. If the
internal rule doesn’t meet your specific needs for numerical
accuracy or performance, use one of the following options:

Specify the output data type explicitly.

Use the simple choice of Inherit:
Same as input.

Explicitly specify a default data type such as
fixdt(1,32,16) and then use the
Fixed-Point Tool to propose data types for your
model. For more information, see fxptdlg.

To specify your own inheritance rule, use
Inherit: Inherit via back
propagation and then use a Data Type
Propagation block. Examples of how to use
this block are available in the Signal Attributes
library Data Type Propagation
Examples block.

Inherit: Inherit via back
propagation — Use data type of the driving
block.

Select this parameter to prevent the fixed-point tools from overriding the
Output data type you specify on the block. For more
information, see Use Lock Output Data Type Setting (Fixed-Point Designer).

Your model has possible overflow, and you want explicit
saturation protection in the generated code.

Overflows saturate to either the minimum or maximum value that
the data type can represent.

The maximum value that the int8 (signed,
8-bit integer) data type can represent is 127. Any block
operation result greater than this maximum value causes overflow
of the 8-bit integer. With the check box selected, the block
output saturates at 127. Similarly, the block output saturates
at a minimum output value of -128.

Overflows wrap to the appropriate value that is representable
by the data type.

The maximum value that the int8 (signed,
8-bit integer) data type can represent is 127. Any block
operation result greater than this maximum value causes overflow
of the 8-bit integer. With the check box cleared, the software
interprets the overflow-causing value as
int8, which can produce an unintended result.
For example, a block result of 130 (binary 1000 0010) expressed
as int8, is -126.

When you select this check box, saturation applies to every internal operation on the block, not just the output, or result. Usually, the code generation process can detect when overflow is not possible. In this case, the code generator does not produce saturation code.

HDL Architecture

HDL Block Properties

If you use the block in matrix multiplication mode, you can specify the
DotProductStrategy. This setting determines whether you want to
implement the matrix multiplication by using a tree of adders and multipliers, or use the
Multiply-Accumulate block implementation. The default is Fully Parallel.
For more information, see DotProductStrategy (HDL Coder).

Number of registers to place at
the outputs by moving existing delays within your design. Distributed
pipelining does not redistribute these registers. The default is
0. For more details, see ConstrainedOutputPipeline (HDL Coder).

DSPStyle

Synthesis attributes for multiplier mapping. The default is none.
See also DSPStyle (HDL Coder).

InputPipeline

Number of input pipeline stages
to insert in the generated code. Distributed pipelining and constrained
output pipelining can move these registers. The default is
0. For more details, see InputPipeline (HDL Coder).

OutputPipeline

Number of output pipeline stages
to insert in the generated code. Distributed pipelining and constrained
output pipelining can move these registers. The default is
0. For more details, see OutputPipeline (HDL Coder).

Native Floating Point

HandleDenormals

Specify whether you want HDL Coder to insert additional logic to handle denormal numbers in your design.
Denormal numbers are numbers that have magnitudes less than the smallest floating-point
number that can be represented without leading zeros in the mantissa. The default is
inherit. See also HandleDenormals (HDL Coder).

LatencyStrategy

Specify whether to map the blocks in your design to inherit,
Max, Min, Zero, or
Custom for the floating-point operator. The default is
inherit. See also LatencyStrategy (HDL Coder).

NFPCustomLatency

To specify a value, set LatencyStrategy to
Custom. HDL Coderadds latency equal to the value that you specify for the
NFPCustomLatency setting. See also NFPCustomLatency (HDL Coder).

MantissaMultiplyStrategy

Specify how to implement the mantissa multiplication operation during code generation.
By using different settings, you can control the DSP usage on the target FPGA device.
The default is inherit. See also MantissaMultiplyStrategy (HDL Coder).

Complex Data Support

The default (linear) implementation supports complex data.

Complex division is not supported. For block
implementations of the Product block in divide mode or reciprocal mode, see
HDL Code Generation on the
Divide block reference page.

Restrictions

HDL code generation does not support more than two inputs at the ports of the
block when you use the block in matrix multiplication mode.

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